Nonparametric inference of doubly stochastic Poisson process data via the kernel method. (English) Zbl 1220.62037

Summary: Doubly stochastic Poisson processes, also known as the Cox processes, frequently occur in various scientific fields. In this article, motivated primarily by analyzing Cox process data in biophysics, we propose a nonparametric kernel-based inference method. We conduct a detailed study, including an asymptotic analysis, of the proposed method, and provide guidelines for its practical use, introducing a fast and stable regression method for bandwidth selection. We apply our method to real photon arrival data from recent single-molecule biophysical experiments, investigating proteins’ conformational dynamics. Our result shows that conformational fluctuation is widely present in protein systems, and that the fluctuation covers a broad range of time scales, highlighting the dynamic and complex nature of proteins structure.


62G07 Density estimation
62M09 Non-Markovian processes: estimation
92C05 Biophysics
62E20 Asymptotic distribution theory in statistics
62P35 Applications of statistics to physics


KernSmooth; sm
Full Text: DOI arXiv


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